Quantum Probability as a Generalized Logical Structure: From Interference Statistics to Quantum Logic and the Classical Limit

Viktoras Rimsha, Laimontas Rimsha

Published Dec 23, 2025• 0 citations

Abstract

In this paper we propose a unified conceptual framework in which quantum probability, quantum logic, and classical probability theory are understood as different structural levels of a single theoretical hierarchy. Starting from a statistical interpretation of quantum interference, previously developed by the authors, we argue that quantum probability is not an alternative to classical Kolmogorov probability, but a more general structure. Classical probability theory emerges as a limiting case corresponding to the disappearance of interference and the effective decomposition of the whole into independent elements. Within this framework, the Birkhoff–von Neumann quantum logic appears as a natural logical expression of quantum probability rather than as an abstract algebraic construction detached from physical meaning. The priority of the whole over its parts plays a central role in both quantum probability and quantum logic, while classical logic and probability arise when this priority becomes trivial. We emphasize that the proposed interpretation does not reject existing quantum formalism, but reinterprets its logical and probabilistic foundations. This approach may have implications for the conceptual understanding of quantum algorithms and quantum information processing.

DOI: 10.5281/zenodo.18037048

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